Institute of MathematicsNorthern Jiaotong University

ORIGINAL ARTICLES

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DOI:
10.1007/s101149900030

Cite this article as:

Chang, Y. Acta Math Sinica (2000) 16: 103. doi:10.1007/s101149900030

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Abstract

Given any positive integers k≥ 3 and λ, let c(k, λ) denote the smallest integer such that v∈B(k, λ) for every integer v≥c(k, λ) that satisfies the congruences λv(v− 1) ≡ 0(mod k(k− 1)) and λ(v− 1) ≡ 0(mod k− 1). In this article we make an improvement on the bound of c(k, λ) provided by Chang in [4] and prove that \(
c{\left( {k,\lambda } \right)} \leqslant \exp {\left\{ {k^{{3k^{6} }} } \right\}}
\). In particular, \(
c{\left( {k,1} \right)} \leqslant \exp {\left\{ {k^{{k^{2} }} } \right\}}
\).